A GRASP/Path Relinking algorithm for two- and three-dimensional multiple bin-size bin packing problems

2013 ◽  
Vol 40 (12) ◽  
pp. 3081-3090 ◽  
Author(s):  
R. Alvarez-Valdes ◽  
F. Parreño ◽  
J.M. Tamarit
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Path Relinking ◽  
Packing Problems

scholarly journals Automating the Packing Heuristic Design Process with Genetic Programming

2012 ◽  
Vol 20 (1) ◽  
pp. 63-89 ◽  
Author(s):  
Edmund K. Burke ◽  
Matthew R. Hyde ◽  
Graham Kendall ◽  
John Woodward
Keyword(s):  
Genetic Programming ◽  
Design Process ◽  
Design Methodology ◽  
Bin Packing ◽  
Three Dimensional ◽  
Programming System ◽  
Problem Type ◽  
Packing Problems ◽  
Design Heuristics ◽  
Design Heuristic

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains.

scholarly journals Erratum to “The Three-Dimensional Bin Packing Problem”: Robot-Packable and Orthogonal Variants of Packing Problems

2005 ◽  
Vol 53 (4) ◽  
pp. 735-736 ◽  
Author(s):  
Edgar den Boef ◽  
Jan Korst ◽  
Silvano Martello ◽  
David Pisinger ◽  
Daniele Vigo
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Packing Problems ◽  
Bin Packing Problem

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

Lower bounds for three-dimensional multiple-bin-size bin packing problems

OR Spectrum ◽  
2013 ◽  
Vol 37 (1) ◽  
pp. 49-74 ◽  
Author(s):  
R. Alvarez-Valdes ◽  
F. Parreño ◽  
J. M. Tamarit
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problems

The Improvement of a Hybrid Genetic Algorithm for Three Dimensional Bin-Packing Problems

2012 ◽  
Vol 200 ◽  
pp. 470-473
Author(s):  
Zhen Zhai ◽  
Li Chen ◽  
Xiao Min Han
Keyword(s):  
Genetic Algorithm ◽  
Bin Packing ◽  
Hybrid Genetic Algorithm ◽  
Three Dimensional ◽  
Packing Problem ◽  
Flow Process ◽  
Packing Problems ◽  
Loading Problem ◽  
The Cost ◽  
Process Diagrams

The multi-constrained bi-objective bin packing problem has many extensive applications. In the loading section of logistics it has mainly been transported by truck. The cost of transportation is not only determined by the bin space utilization, but also by the number of vehicles in transporta¬tion utilization. The type of items and bins is introduced in the mathematical model, as well as the volume of the items. In this paper, the hybrid genetic algorithm which tabu and simulated annealed rules are added for complex container-loading problem is studied. The effective coding and decod-ing method together with flow process diagrams are given.

scholarly journals Two and three-dimensional bin packing problems : an efficient implementation of evolutionary algorithms

2018 ◽  
Author(s):  
◽  
Andile Ntanjana
Keyword(s):  
Genetic Algorithm ◽  
Polynomial Time ◽  
Heuristic Algorithm ◽  
Bin Packing ◽  
Optimization Problems ◽  
Research Work ◽  
Three Dimensional ◽  
Second Phase ◽  
Packing Problems ◽  
Elitist Strategy

The present research work deals with the implementation of heuristics and genetic algo- rithms to solve various bin packing problems (BPP). Bin packing problems are a class of optimization problems that have numerous applications in the industrial world, ranging from efficient cutting of material to packing various items in a larger container. Bin packing problems are known to be non-deterministic polynomial-time hard (NP-hard), and hence it is impossible to solve them exactly in polynomial time. Thus heuristics are very important to design practical algorithms for such problems. In this research we avoid the use of linear programming because we consider it to be a very cumbersome approach for analysing these types of problems and instead we proposed a simple and very efficient algorithm which is a combination of the fi fi heuristic algorithm in combination with the genetic algorithm, to solve the two and three – dimensional bin packing problems. The packing was carried out in two phases, wherein the fi phase the bins are packed by means of the fi fi heuristic algorithm with the help of other auxiliary techniques, and in the second phase the genetic algorithm is implemented. The purpose of the second phase is to improve the initial arrangements by performing combinatorial optimization for either a limited number of bins or the whole set at one time without destroying the original pattern (elitist strategy). The programming code developed can be used to write high-speed and capable software, which can be used in real-time applications. To conclude, the developed optimization ap- proach signifi tly helps to handle the bin packing problem. Numerical results obtained by optimizing existing industrial problems demonstrated that in many cases it was possible to achieve the optimum solution within only a few seconds, whereas for large-scale complex problems the result was near optimum efficiency over 90% within the same period of time.

Packing Optimization by Enhanced Rubber Band Analogy

2005 ◽  
Author(s):  
Hong Dong ◽  
Georges M. Fadel ◽  
Vincent Y. Blouin
Keyword(s):  
Three Dimensional ◽  
Optimization Method ◽  
Rubber Band ◽  
Volume Relaxation ◽  
New Developments ◽  
Packing Problems ◽  
Rubber Balloon ◽  
Elastic Forces ◽  
Reaction Forces ◽  
Packing Optimization

In this paper, some new developments to the packing optimization method based on the rubber band analogy are presented. This method solves packing problems by simulating the physical movements of a set of objects wrapped by a rubber band in the case of two-dimensional problems or by a rubber balloon in the case of three-dimensional problems. The objects are subjected to elastic forces applied by the rubber band to their vertices as well as reaction forces when contacts between objects occur. Based on these forces, objects translate or rotate until maximum compactness is reached. To improve the compactness further, the method is enhanced by adding two new operators: volume relaxation and temporary retraction. These two operators allow temporary volume (elastic energy) increase to get potentially better packing results. The method is implemented and applied for three-dimensional arbitrary shape objects.

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